Linear analysis of intensity level histograms is proposed as a method to determine the area fractions of homogeneous components of images. The area fractions are the coefficients of the respective histograms in the linear combination that best fits the histogram of the entire image. This method can be applied whenever the components can be identified by their individual histograms which must be linearly independent. Its accuracy was tested for images of real surfaces that were edited to contain known fractions of the components, and it proved to be suitable for the analysis of images made of textured components that show large overlapping of their histograms.